The double-helical DNA of large eukaryotic genomes is tightly compacted within the tiny cell nucleus as a DNA–protein complex, chromatin. The universal elements of chromatin, nucleosome core particles (NCPs, 147 base pairs of DNA wrapped around an octamer of histone proteins), are connected by linker DNA of variable lengths into nucleosome arrays, which fold into various and dynamic higher-order structures. Since DNA is a highly negatively charged polyelectrolyte, electrostatic interactions of DNA with positively charged histones, other charged nuclear proteins, as well as with monovalent and multivalent cations, contributes decisively to the formation and folding of nucleosome arrays. The dimensions and timescales of cellular chromatin states and transformations necessitate a multiscale coarse-graining (CG) approach to understand their properties through computational modeling. In this review, we highlight the importance of electrostatics for NCP interactions and nucleosome fiber folding in vitro and in vivo, and argue that the inclusion of explicit ions is indispensable for accurate CG modeling of chromatin structure and dynamics. A summary of the existing CG mapping and force field setups is provided. A brief account of CG modeling studies in which salt dependency is approximated by the Debye–Hückel treatment is given. The primary focus is on the presentation of results from papers that include explicit monovalent and multivalent ionic species in CG simulations of nucleosomes and nucleosome arrays. Finally, we underline perspectives and challenges for future multiscale computational modeling of chromatin.